$A$ $NPN$ transistor conducts when

Given below are two statements:
Statement $I :$ $PN$ junction diodes can be used to function as a transistor,simply by connecting two diodes back-to-back,which acts as the base terminal.
Statement $II :$ In the study of transistors,the amplification factor $\beta$ indicates the ratio of the collector current to the base current.
In the light of the above statements,choose the correct answer from the options given below:

For a transistor amplifier,the power gain and voltage gain are $7.5$ and $2.5$ respectively. The value of the current gain will be:

For a constant collector-emitter voltage of $8\,V$,the collector current of a transistor changed from $4\,mA$ to $6\,mA$,whereas the base current changed from $20\,\mu A$ to $25\,\mu A$. If the transistor is in the active state,the small signal current gain (current amplification factor) will be:

The input resistance of a silicon transistor is $100\,\Omega$. Base current is changed by $40\,\mu A$,which results in a change in collector current by $2\,mA$. This transistor is used as a common emitter amplifier with a load resistance of $4\,k\Omega$. The voltage gain of the amplifier is:

$10^{10}$ electrons enter the emitter of a junction transistor in a time of $0.4 \mu s$. If $5 \%$ of the electrons are lost in the base, then the collector current is (in $\text{ mA}$)